Mathematics

Global Existence, Uniqueness and Regularity of Solutions to a von Karman System With Nonlinear Boundary Dissipation Angelo Favini Dipartimento di Matematica University di Bologna Piazza di Porta S. Donato 5 40127 Bologna, Italy Irena Lasiecka Department of Applied ...

Background. Methicillin-resistant Staphylococcus aureus (MRSA) has traditionally been associated with infections in hospitals. Recently, a new strain of MRSA has emerged and rapidly spread in the community, causing serious infections among young, healthy individuals. Preliminary reports imply that a particular clone (USA300) of a community-acquired MRSA (CA-MRSA) strain is infiltrating hospitals and replacing the traditional hospitalacquired MRSA strains. If true, this event would have serious consequences, because CA-MRSA infections in hospitals would occur among a more debilitated, older patient population. Methods. A deterministic mathematical model was developed to characterize the factors contributing to the replacement of hospital-acquired MRSA with CA-MRSA and to quantify the effectiveness of interventions aimed at limiting the spread of CA-MRSA in health care settings. Results. The model strongly suggests that CA-MRSA will become the dominant MRSA strain in hospitals and health care facilities. This reversal of dominant strain will occur as a result of the documented expanding community reservoir and increasing influx into the hospital of individuals who harbor CA-MRSA. Competitive exclusion of hospital-acquired MRSA by CA-MRSA will occur, with increased severity of CA-MRSA infections resulting in longer hospitalizations and a larger in-hospital reservoir of CA-MRSA. Conclusions. Improving compliance with hand hygiene and screening for and decolonization of CA-MRSA carriers are effective strategies. However, hand hygiene has the greatest return of benefits and, if compliance is optimized, other strategies may have minimal added benefit.

Recently, we (D'Agata et al., Modeling the invasion of community-acquired methicillinresistant Staphylococcus aureus into the hospital setting, submitted) proposed a deterministic mathematical model to characterize the factors contributing to the replacement of hospitalacquired methicillin-resistant Staphylococcus aureus (HA-MRSA) with the community-acquired methicillin-resistant Staphylococcus aureus (CA-MRSA) and to quantify the effectiveness of interventions aimed at limiting the spread of CA-MRSA in the hospital setting. Numerical simulations of the model strongly suggest that CA-MRSA will become the dominant MRSA strain in the hospital setting. In this companion paper, we provide mathematical analysis and more numerical simulations of the model. It is shown that when no colonized or infected patients enter the hospital, competitive exclusion of HA-MRSA by CA-MRSA will occur with increased severity of CA-MRSA infections resulting in longer hospitalizations and a larger inhospital reservoir of CA-MRSA. Improving compliance with hand hygiene and decolonization of CA-MRSA carriers are effective control strategies.

Background. Mathematical modeling can be used to describe the interdependent and dynamic interactions that contribute to the transmission dynamics of vancomycin-resistant enterococci (VRE). A model was developed to quantify the contribution of antibiotic exposure and of other modifiabl factors to the dissemination of VRE in the hospital setting. Methods. The model consists of 4 compartments: patients colonized with VRE receiving and not receiving antibiotics and uncolonized patients receiving and not receiving antibiotics. A series of differential equations describe the movement between these compartments. Baseline parameter estimates were obtained from pharmacy, infectioncontrol, and clinical databases. Results. The main predictions of this model are that (1) preventing the initiation or enhancing the discontinuation of unnecessary antimicrobial therapy will have a greater impact if it is targeted to patients who are not colonized with VRE; (2) increasing the number of patients harboring VRE at the time of hospital admission substantially increases the endemic prevalence of VRE; and (3) eliminating the influ of VRE results in the eradication of this pathogen from the hospital. A decrease in the endemic prevalence of VRE also occurs with a decrease in the length of hospital stay of colonized patients, increased hand hygiene compliance, and a lower ratio of healthcare workers:patients. Conclusion. This mathematical model provides a framework to assist in targeting necessary interventions aimed at limiting the spread of VRE. Despite efforts to prevent the cross-transmission of vancomycin-resistant enterococci (VRE) between hospitalized patients, rates of vancomycin resistance among enterococci continue to increase [1]. This persistent increase may reflec an incomplete understanding of the complexities of the transmission dynamics of VRE and of the contribution of antibiotic exposure to the increase in both the likelihood of VRE acquisition and

The transmission dynamics of vancomycin-resistant enterococci (VRE) and factors contributing to their dissemination are complex. Mathematical modeling was used to simulate patterns of dissemination among patients and health care workers (HCWs) and to quantify the contribution of specific factors and infection control interventions on the endemic prevalence (EP) of VRE in a long-term hemodialysis unit. The model predicted that (1) an EP of 12% would be reached over time, regardless of the number of patients initially colonized, (2) endemicity would be sustained by the constant influx of newly colonized patients discharged from the hospital, (3) duration of VRE gastrointestinal colonization would have the most impact on the number of secondary cases, increasing the EP to a maximum of 70%, and (4) decreasing the patient:HCW ratio or improving hand hygiene would decrease the EP to 3%. Decreasing the duration of colonization, limiting hospital acquisition of VRE, and improving compliance with hand hygiene in the hemodialysis unit may decrease the rapidly rising rates of VRE in the patient population.

Uniform exponential decay of solution is established for the elastodynamic system of elasticity using boundary feedback control. Energy dissipation is introduced via linear velocity feedbacks acting through a portion of the boundary as traction forces. Two primary goals are achieved: First, these results are proven without the imposition of strong geometric assumptions on the controlled portion of the boundary, thus extending earlier work which required that the domain be ''star shaped.'' Second, the feedback is only a function of velocity, as opposed to also containing the tangential derivative of the displacement, resulting in a physically viable feedback. Proof is based on the multiplier method and relies critically on sharp trace estimates for the tangential derivative of the displacement on the boundary as well as on unique continuation results for the corresponding static system.

A mathematical model of the G protein signaling pathway in RAW 264.7 macrophages downstream of P2Y 6 receptors activated by the ubiquitous signaling nucleotide uridine 5′-diphosphate is developed. The model, which is based on time-course measurements of inositol trisphosphate, cytosolic calcium, and diacylglycerol, focuses particularly on differential dynamics of multiple chemical species of diacylglycerol. When using the canonical pathway representation, the model predicted that key interactions were missing from the current network structure. Indeed, the model suggested that accurate depiction of experimental observations required an additional branch to the signaling pathway. An intracellular pool of diacylglycerol is immediately phosphorylated upon stimulation of an extracellular receptor for uridine 5′-diphosphate and subsequently used to aid replenishment of phosphatidylinositol. As a result of sensitivity analysis of the model parameters, key predictions can be made regarding which of these parameters are the most sensitive to perturbations and are therefore most responsible for output uncertainty.

A v on K arm an system with feedback control acting through the boundary as a bending moment only is considered. In addition to establishing uniform decay rates for the solution to this model, we show that the control is robust with respect to a parameter, , appearing in our system. This parameter is directly proportional to the thickness of the plate and is therefore assumed to be very small, however, since it corresponds to a portion of the principal part of the dierential operator, neglecting this term would signicantly change the properties of the solution. To prove our solution decays uniformly independently of , w e begin by using multiplier methods to nd preliminary energy estimates. Next, we apply \sharp" trace regularity results to obtain the desired energy estimate, modulo traces of the von K arm an nonlinearity and lower order terms. These terms are absorbed by an appropriately developed nonlinear compactness/uniqueness argument. Finally, application of nonlinear semigroup theory completes the proof.

A model comprised of a nonlinear von Kármán plate coupled with a nonlinear beam equation is developed from first principles. Dynamic junction conditions are imposed at the interface. Wellposedness is established by first considering a corresponding linear problem, then applying a perturbation theorem for nonlinear semigroups. Proof of regularity takes advantage of elliptic theory, as well as the regularity of the Airy's stress function. The compatibility constraints at the junction give rise to mathematical challenges not seen in earlier work on the individual plate and beam models.

Asymptotic behavior of solutions to a von Karrmin model with y = 0; i.e., without accounting for rotational forces, is considered. It is shown that in the presence of nonlinear boundary damping all weak solutions decay to zero uniformly in the energy norm.

Multidrug-resistant organisms (MDRO) continue to spread in hospitals globally, but the population-level impact of recommended preventive strategies and the relative benefit of individual strategies targeting all MDRO in the hospital setting are unclear. To explore the dynamics of MDRO transmission in the hospital, we develop a model extending data from clinical individual-level studies to quantify the impact of hand hygiene, contact precautions, reducing antimicrobial exposure and screening surveillance cultures in decreasing the prevalence of MDRO colonization and infection. The effect of an ongoing increase in the influx of patients colonized with MDRO into the hospital setting is also quantified. We find that most recommended strategies have substantial effect in decreasing the prevalence of MDRO over time. However, screening for asymptomatic MDRO colonization among patients who are not receiving antimicrobials is of minimal value in reducing the spread of MDRO.

The aim of this paper is to consider a physically valid and meaningful model of the Euler-Bernoulli plate with boundary conditions which include moments of inertia realistically present in the system. For this model, we shall prove that the appropriately selected boundary feedback uniformly stabilizes the model, i.e., the energy decays to zero uniformly when t-+ oo. Our choice of boundary feedback is motivated by the fact that boundary controls are easily implemented as the need to act only on the bundary of the spatial domain. Inclusion of the moments of inertia in the model is a source of serious mathematical difficulties when deriving the appropriate estimates for stabilization. We shall need, as a preliminary step of analysis, to develop new regularity results for the traces of the solution to special types of plate problems. These regularity results together with sharp energy estimates allow us to prove that uniform stabilization holds.

Background There had been a preliminary occurrence of human-to-human transmissions between healthcare workers (HCWs), but risk factors in the susceptibility for COVID-19, and infection patterns among HCWs have largely remained unknown. Methods Retrospective data collection on demographics, lifestyles, contact status with infected subjects for 118 HCWs (include 12 COVID-19 HCWs) from a single-center. Sleep quality and working pressure were evaluated by Pittsburgh Sleep Quality Index (PSQI) and The Nurse Stress Index (NSI), respectively. Follow-up duration was from Dec 25, 2019, to Feb 15, 2020. Risk factors and transmission models of COVID-19 among HCWs were analyzed and constructed. Findings A high proportion of COVID-19 HCWs had engaged in night shift-work (75.0% vs. 40.6%) and felt they were working under pressure (66.7% vs. 32.1%) than uninfected HCWs. COVID-19 HCWs had higher total scores of PSQI and NSI than uninfected HCWs. Furthermore, these scores were both positively associ...

In this paper both deterministic and stochastic models are developed to explore the roles that antibiotic exposure and environmental contamination play in the spread of antibiotic-resistant bacteria, such as methicillin-resistant Staphylococcus aureus (MRSA), in hospitals. Uncolonized patients without or with antibiotic exposure, colonized patients without or with antibiotic exposure, uncontaminated or contaminated healthcare workers, and free-living bacteria are included in the models. Under the assumption that there is no admission of the colonized patients, the basic reproduction number R 0 is calculated. It is shown that when R 0 < 1, the infection-free equilibrium is globally asymptotically stable; when R 0 > 1, the infection is uniformly persistent. Numerical simulations and sensitivity analysis show that environmental cleaning is a critical intervention, and hospitals should use antibiotics properly and as little as possible. The rapid and efficient treatment of colonized patients, especially those with antibiotic exposure, is key in controlling MRSA infections. Screening and isolating colonized patients at admission, and improving compliance with hand hygiene are also important control strategies.